Beautiful Discovery with Nature's Patterns

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Beautiful Discovery with Nature's Patterns DeCODE nature's beauty. Beautiful Math, Code & Art. Deep looking through art and science. We offer Rekindle awe & wonder.

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05/06/2026

Rose of Venus-Earth Orbits

The ratio of orbital speeds of Venus and Earth are 8 to 13, resulting in this five petaled rose pattern.

Did this with simple Scratch code blocks so you can see how it is done and change it up your way (see comment for link)

Kept color range close to rose red.

Near the inner loops, we see apparent retrograde motion where Venus seems to move backward in the sky from our viewpoint on Earth. There, Venus seems to pause, then move “backward” (westward) relative to background stars, before pausing and resuming its eastward motion.

For simplification, we assume Venus and Earth are in coplanar concentric perfect circular orbits, with orbital periods in an exact 8:13 ratio.

Planet images enlarged for visualization (not to scale).

27/05/2026

Uses phi, the golden ratio, in the turn angle of spirals and in the coloring

Phi, the golden ratio, is called the "most irrational number" because it is the hardest to approximate using simple fractions. According to Hurwitz's theorem, numbers like Pi can be easily approximated by fractions, but Phi actively resists this. For the same reason, Phi beautifully fills the space in this space, just as it fills most efficiently fills a sunflower or daisy head with florets.

Change it up your way in Scratch here: https://scratch.mit.edu/projects/1313307369/


16/05/2026

Another of our projects featured today:

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Now over 8,000 loves and many tens of thousands of thoughtful comments on favorite settings. We do a project almost ever...
18/04/2026

Now over 8,000 loves and many tens of thousands of thoughtful comments on favorite settings. We do a project almost every day but can never predict what will resonate

08/03/2026

Pendulum Dance - Harmonic Waves

Scratch featured this project!

Different pendulum lengths have different swing speeds. The speed is inversely proportional to square-root of length. Each pendulum has a slightly longer length than previous so goes a bit slower. So, the pendulums' traveling wave patterns gradually go out of phase then back in phase.

Wait long enough for pendulums to align again. The pattern repeats with variations between.

Toy model versions are widely available, but they eventually stop swinging.

See comment for link to our Scratch model, from which we coded the pendulums and made this movie.

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https://www.facebook.com/share/p/1DVquGGbm7/
25/02/2026

https://www.facebook.com/share/p/1DVquGGbm7/

As of February 4, 2026, Voyager 1 is approximately 15.95 billion miles (25.6 billion km) from Earth, continuing its lonely trek through interstellar space. This distance is so vast that light—the fastest thing in the universe—takes about 23 hours and 34 minutes to travel one way between the probe and NASA’s Deep Space Network. The spacecraft is rapidly approaching a major "light-day" milestone, expected in November 2026, when it will be exactly one light-day (16.1 billion miles) away, meaning a round-trip communication will require two full days. Despite being nearly 50 years old and operating on a dwindling nuclear power source, Voyager 1 recently resumed regular science operations after engineers successfully troubleshot a radio transmitter issue and a computer glitch in the Flight Data Subsystem (FDS).

Einstein didn't work and study in the traditional way, but rather took many naps, played violin, took long walks, and da...
21/02/2026

Einstein didn't work and study in the traditional way, but rather took many naps, played violin, took long walks, and daydreamed. He believed all these boosted creativity and cognitive function, but also valued these as inherent joys.

Einstein was famous on campus for taking long daily walks in Princeton, typically in the woods or through residential streets. Einstein saw rest, long walks, and playing violin as vital to his creative process. "If I were not a physicist, I would probably be a musician. I often think in music. I live my daydreams in music. I see my life in terms of music... I get most joy in life out of my violin." (Albert Einstein, in a 1929 interview with George Sylvester Viereck). Notice he links his creativity to his music but, crucially, his violin was an inherent joy, in fact here he says it was his main joy.

His second wife, Elsa, noted: "Music helps him when he is thinking about his theories. He goes to his study, comes back, strikes a few chords on the piano, jots something down, returns to his study."

On taking walks, he wrote in a letter to his youngest son (Eduard, written in German June 1918): "Make a lot of walks to get healthy and don't read that much but save yourself some until you're grown up."

Einstein didn't worry about wasting time. He believed that forcing work was less productive than allowing the mind to wander. "Creativity is the residue of time wasted."

He was a virtuoso daydreamer.

Einstein's daydreaming (sounds better than "Gedankenexperiments") were his imaginative thought experiments, mental simulations he used to break from classical mechanics and visualize complex physics, driving his revolution in science. Through deep, often solitary, visualization—like chasing light or imagining falling elevators—he established the foundations for special and general relativity.

18/02/2026
Frost ferns on our window
10/02/2026

Frost ferns on our window

05/02/2026

Make a Mobius Strip. Like an "infinity boardwalk", you could walk all along it and find there's only one side.

It's one-sided ruled-surface, made of straight sticks.





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